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Mechanistic interpretability seeks to reverse-engineer neural network computations into human-understandable algorithms, yet extracting sparse computational circuits from billion-parameter language models remains challenging due to…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
Many real-world data can be represented as heterogeneous graphs with different types of nodes and connections. Heterogeneous graph neural network model aims to embed nodes or subgraphs into low-dimensional vector space for various…
Algebraic multigrid (AMG) is conventionally applied in a black-box fashion, agnostic to the underlying geometry. In this work, we propose that using geometric information -- when available -- to assist with setting up the AMG hierarchy is…
Visual recognition relies on understanding the semantics of image tokens and their complex interactions. Mainstream self-attention methods, while effective at modeling global pair-wise relations, fail to capture high-order associations…
Solving Algebra Problems with Geometry Diagrams (APGDs) is still a challenging problem because diagram processing is not studied as intensively as language processing. To work against this challenge, this paper proposes a hologram reasoning…
This paper introduces a geometric representation of hypergraphs by representing hyperedges as simplices. Building on this framework, we employ homotopy groups to analyze the topological structure of hypergraphs embedded in high-dimensional…
Hypergraphs play a pivotal role in the modelling of data featuring higher-order relations involving more than two entities. Hypergraph neural networks emerge as a powerful tool for processing hypergraph-structured data, delivering…
Hypergraph offers a framework to depict the multilateral relationships in real-world complex data. Predicting higher-order relationships, i.e hyperedge, becomes a fundamental problem for the full understanding of complicated interactions.…
Evaluating node importance is a critical aspect of analyzing complex systems, with broad applications in digital marketing, rumor suppression, and disease control. However, existing methods typically rely on conventional network structures…
Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space. Existing KG embedding approaches model entities andrelations in a KG by utilizing real-valued ,…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, and joint interactions of proteins, to name a few. In this work, we propose tools for answering…
While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…
In this paper we present a new semidefinite programming hierarchy for covering problems in compact metric spaces. Over the last years, these kind of hierarchies were developed primarily for geometric packing and for energy minimization…
Persistent homology (PH) is one of the most popular tools in topological data analysis (TDA), while graph theory has had a significant impact on data science. Our earlier work introduced the persistent spectral graph (PSG) theory as a…
Three-dimensional scene generation holds significant potential in gaming, film, and virtual reality. However, most existing methods adopt a single-step generation process, making it difficult to balance scene complexity with minimal user…
In this article we present a new and not fully employed geometric algebra model. With this model a generalization of the conformal model is achieved. We discuss the geometric objects that can be represented. Furthermore, we show that the…
Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…